RMS Describing, Resampling, Validating, and Simplifying the Model

@Tripartio GLM does not assume linearity so I am not comfortable with the framing of the question. And beware of “average effect” as the estimated effects are conditional on other predictors and on the interaction being zero. Partial effect plots can replace coefficients in a sense, if there are no interactions or the interactions are with discrete variables (or there are 2 continuous variables interacting and you make a 3D graph, which can be hard to estimate predicted values from).

Thanks @s_doi and @f2harrell for your responses. But isn’t the issue about interactions exactly the same with coefficients? Aren’t GLM coefficients likewise only meaningful “if there are no interactions”? That is, I do not see partial effect plots as a disadvantage compared to coefficients in this sense–they just share the same caution.

Your framing of the question makes it seem as if partial effect plots are a stand-alone method for estimating a relationship between a predictor X and an outcome Y, but they’re not. Partial effect plots are just visualizations of quantities calculated from a fitted model. In fact, the reliance of a partial effects plot on a particular fitted model is right there in the rms code you wrote: ggplot(Predict(model)). So it’s not true that “partial effects plots…visualize relationships of any shape with no need to assume the distribution of the X or the Y variable”. The visualized relationships in the plot will reflect whatever assumptions you made in your model. The relationship it shows between the predictor and the outcome will capture the true relationship only to the extent that the underlying model does. And, as Frank mentioned, GLMs do not assume linear relationships between predictors and outcomes, and can in fact incorporate flexible modeling of non-linear relationships via restricted cubic splines.

In addition to that excellent reply, it’s helpful to think more generally than main effects and interactions and to assume that interaction effects are carried along into any estimate that is meaningful.

@Tripartio, you have hit upon an important point here. When a predictor X is associated with multiple terms in the model (e.g. because of interactions or modeling via polynomials or splines), then the individual coefficients may no longer correspond to meaningful quantities by themselves. Instead, meaningful quantities might only emerge when we consider multiple coefficients at a time. That is where things like plots of predicted values can be much more informative about the relationship between X and Y than say a table of estimated regression coefficients.

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And chunk tests, e.g. testing whether one predictor interacts when any of three other predictors, are appropriate.